Abstract

A broad class of astronomical accretion disks is presently shown to be
dynamically unstable to axisymmetric disturbances in the presence of a
weak magnetic field, an insight with consequently broad applicability to
gaseous, differentially-rotating systems. In the first part of this
work, a linear analysis is presented of the instability, which is local
and extremely powerful; the maximum growth rate, which is of the order
of the angular rotation velocity, is independent of the strength of the
magnetic field. Fluid motions associated with the instability directly
generate both poloidal and toroidal field components. In the second part
of this investigation, the scaling relation between the instability's
wavenumber and the Alfven velocity is demonstrated, and the independence
of the maximum growth rate from magnetic field strength is confirmed.